WASHINGTON — The line of mourners snaked through the Capitol: little children resting on their parents’ shoulders, retirees from North Carolina, the manager of a recreational vehicle dealership who flew in from Houston, the leader of a Muslim Boy Scout troop in Virginia. They filed past the plain pine plywood coffin in the grand Capitol Rotunda, some weeping, most in quiet contemplation.

“I feel like he’s the Martin Luther King of our day,’’ said Sam Bass, 36, the recreational vehicle salesman, gazing at the simple coffin.

“He was like Jesus for us,’’ said Diane Busby, 57, who came with a group of friends from Edmond, Oklahoma.

“He” was the Rev. Billy Graham, who died last week at the age of 99 and on Wednesday became only the fourth private citizen in American history to lie in honor at the United States Capitol, as politicians including President Trump, along with hundreds if not thousands of ordinary Americans, came to pay their respects.

“Today in the center of this great chamber lies legendary Billy Graham, an ambassador for Christ who reminded the world of the power of prayer and the gift of God’s grace,” Mr. Trump said in brief remarks during a morning memorial service, before laying a wreath at the coffin of Mr. Graham.

Mr. Graham’s global ministry included close relationships with presidents since Harry Truman. His legacy includes an outsize influence on the life of America by encouraging millions of evangelical Christians to be engaged in social and political activism.

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President Trump placed his hand on the coffin of Mr. Graham.CreditAl Drago for The New York Times

Among those whose lives he changed was former President George W. Bush, who wrote in The Wall Street Journal that Mr. Graham’s “care and his teachings were the real beginning of my faith walk — and the start of the end of my drinking.”

Mr. Graham’s simple coffin, made by inmates at the Louisiana State Penitentiary, arrived at the Capitol in a sleek black hearse at 11 a.m., where it was greeted by a military honor guard. Eight pallbearers in dress uniform carried the coffin up the steps and inside the Capitol, where the entrances to the Rotunda were draped in black.

Cabinet officials, senators, House members and family members also gathered Wednesday morning to pay tribute.

Senator Mitch McConnell of Kentucky, the majority leader, called Mr. Graham “a happy instrument in the hands of his creator” and called on the nation to remember him.

“The secret of my work, he explained, is God,” Mr. McConnell said of Mr. Graham. “I would be nothing without Him. That is what made Billy Graham America’s pastor.”

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Senators, House members, cabinet officials and family members also gathered to pay tribute.CreditPool photo by Chip Somodevilla

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Mr. Graham’s coffin will remain in the Capitol Rotunda until Thursday.CreditTom Brenner/The New York Times

Speaker Paul D. Ryan of Wisconsin said Mr. Graham repeatedly challenged the nation to look to God and to look within.

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The public was invited to view the coffin of Mr. Graham.CreditAl Drago for The New York Times

“In those moments, when we felt weak in spirit, when our country was on its knees, he reminded us, he convinced us that is exactly when we find our grace and our strength,” Mr. Ryan said.

Others had more personal remembrances. When Senator Lamar Alexander, Republican of Tennessee, was governor of that state, he played piano at one of Mr. Graham’s revivals in Nashville in 1979. “I played ‘Amazing Grace’ on a nine-foot Steinway,’’ the senator said in an interview after the service.

Mr. Trump, in his remarks, recalled attending a Billy Graham sermon at Yankee Stadium in New York, saying that his father, Fred Trump, was a fan of Mr. Graham’s at the time.

“My father said to me, ‘Come on, son,’ and by the way he said, ‘Come on, mom, let’s go see Billy Graham at Yankee Stadium.’ And it was something very special. But Americans came in droves to hear that great young preacher,” the president said. “Fred Trump was a big fan. Fred Trump was my father.”

And Sekou Austin Davis, 48, an immigrant from Liberia, slipped away from his job as a physical security worker at the Capitol to pay his respects to Mr. Graham. When he was a little boy, he said, his father — who was later executed in a military coup — took him to see Mr. Graham preach.

Mr. Graham joined an exclusive list of more than 30 Americans who have lain in state or in honor in the Rotunda, including lawmakers, presidents, civil rights activists, law enforcement officers killed in the line of duty, an F.B.I. director, military commanders and the remains of unidentified soldiers from several of the nation’s wars. The last private citizen to lie in honor was Rosa Parks, the civil rights leader, in 2005.

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Over the course of his career, the Rev. Billy Graham capitalized on modern communication technologies — from television to satellite to the internet — to give his ministry a global reach.Published OnFeb. 21, 2018CreditCreditWilliam E. Sauro/The New York Times

Though he was a counselor to many presidents throughout many decades, as he preached to packed stadiums and people watching on television around the world, Mr. Graham later eschewed the mixing of politics and religion, saying that he had “crossed the line.”

That sentiment has prompted some to question whether he would have agreed with the decision to have his coffin lie in honor in the Capitol, which perhaps could be viewed as a celebration of the crossing the line that he no longer believed appropriate at the end of his life.

“Of course its appropriate,’’ said Senator John Cornyn of Texas, the No. 2 Republican in the Senate. “Somebody who’s had such an influence on America and Americas leadership in such a positive way — I think its entirely appropriate that he be in honor.”

Mr. Graham’s coffin, which will remain in the Capitol Rotunda until Thursday, rests on a “catafalque,” a wooden stand, which was constructed by the Architect of the Capitol for such ceremonies. After the memorial service, private citizens began lining up to view it.

Among them were Robert Skinner, 74 and his wife Patsy, 71, of Raleigh, North Carolina. They came with a group from their church, where one of Mr. Graham’s daughters, the evangelist Ann Graham Lotz, once taught Sunday school. As the couple walked past Mr. Graham’s coffin, Mrs. Skinner wiped tears from her cheeks.

“We’re so blessed,’’ her husband said, as he patted his wife’s back.

As the mourners filed out of the Rotunda, several members of Mr. Graham’s family formed a small receiving line, greeting visitors and thanking them for coming. Among them was one of Mr. Graham’s grandsons, Will Graham, 43, of Asheville, N.C., who was almost speechless as he surveyed the crowd.

“It’s overwhelming,’’ he said, ‘‘to see the love that my granddaddy has.”

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A military honor guard carried the coffin of Mr. Graham into the U.S. Capitol.CreditAlex Edelman/Agence France-Presse — Getty Images